Factor the expression completely. x^(4)-10x^(2)+21 Answer:

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Factor the expression completely.  x^(4)-10x^(2)+21 Answer:

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Identify Type and Strategy: Identify the type of polynomial and look for a common factoring strategy. This is a quadratic in form, with x^4 as the ＂squared＂ term, x^2 as the ＂linear＂ term, and 21 as the constant. We can treat x^2 as a single variable and factor it as if it were a quadratic equation.Set Up Factoring Format: Set up the expression in a factoring format. We are looking for two binomials that multiply to give x^4 - 10x^2 + 21. The general form will be (x^2 - a)(x^2 - b), where a and b are numbers that multiply to 21 and add up to 10.Find Factors and Sum: Find the factors of 21 that add up to 10. The factors of 21 are 1, 3, 7, and 21. The pair that adds up to 10 is 3 and 7.Write Factored Form: Write the factored form using the factors found. The factored form of the expression is (x^2 - 3)(x^2 - 7).Check Factoring: Check the factoring by expanding the binomials. (x^2 - 3)(x^2 - 7) = x^4 - 7x^2 - 3x^2 + 21 = x^4 - 10x^2 + 21. The expanded form matches the original expression, so the factoring is correct.

Factor the expression completely. $\newline$ $x^{4}-10 x^{2}+21$ $\newline$ Answer:

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Factor the expression completely. $\newline$ $x^{4}-10 x^{2}+21$ $\newline$ Answer: